Dual Reciprocity Boundary Element Analysis for the Graetz Problem in Circular Duct

원형 덕트유동에서의 Graetz 문제에 대한 이중교환 경계요소 해석

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.